Subject: Why this recent change about (-1)^(1/3) ?
From: Michel Talon
Date: Wed, 16 Feb 2011 17:06:56 +0100
Francois Maltey wrote:
> Hello,
>
> I discover Maxima and compare it to Sage or Maple.
>
> I feel that Maxima changes about (-1)^(1/3).
>
> My old maxima is 5.13.0 from an Ubuntu box and is fine,
> but a more recent maxima in Sage is less nice.
> Is there a reason ?
>
> First the (-1)^(1/3)=-1 in the old maxima, and the solve after is right.
>
> (%i2) (-1)^(1/3) ;
> (%o2) - 1
>
> (%i4) solve (3*x^3-9*x+10, x) ;
> sqrt(3) %i 1
> - ---------- - -
> 1/3 sqrt(3) %i 1 2 2
> (%o4) [x = - 3 (---------- - -) - ----------------,
> 2 2 1/3
> 3
> sqrt(3) %i 1
> ---------- - -
> 2 2 1/3 sqrt(3) %i 1 1/3
> 1
> x = - -------------- - 3 (- ---------- - -), x = - 3
> - ----]
> 1/3 2
> 2 1/3
> 3
> 3
>
> Now I call a more recent maxima built in Sage 4.6.1 at 2011-01-11
> This maxima seems to be a 5.22.1 but I'm not sure.
Here i have maxima 5.22.1 (not from sage) and i get the same as you:
(%i1) solve(3*x^3-9*x+10, x) ;
sqrt(3) %i 1
- ---------- - -
1/3 sqrt(3) %i 1 2 2
(%o1) [x = - 3 (---------- - -) - ----------------,
2 2 1/3
3
sqrt(3) %i 1
---------- - -
2 2 1/3 sqrt(3) %i 1 1/3 1
x = - -------------- - 3 (- ---------- - -), x = - 3 -
----]
1/3 2 2
1/3
3 3
(%i2) (-1)^(1/3) ;
(%o2) - 1
--
Michel Talon